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Set-Valued Means of Random Particles

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Abstract

Planar images of powder particles or sand grains can be interpreted as “figures”, i.e., equivalence classes of directlycongruent compact sets. The paper introduces a concept of set-valuedmeans and real-valued variances for samples of such figures. Inobtaining these results, the images are registered to have similarlocations and orientations. The method is applied to find a mean figure of a sample of polygonal particles.

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Authors and Affiliations

  1. TU Bergakademie Freiberg, D-09596, Freiberg (Sachs), Germany

    Dietrich Stoyan

  2. Department of Statistics, University of Glasgow, Glasgow, G12 8QW, Scotland, UK

    Ilya S. Molchanov

Authors
  1. Dietrich Stoyan
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  2. Ilya S. Molchanov
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Stoyan, D., Molchanov, I.S. Set-Valued Means of Random Particles. Journal of Mathematical Imaging and Vision 7, 111–121 (1997). https://doi.org/10.1023/A:1008289104136

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